Curve-fitting Project -Linear Model (due at the end of Week 5)

Instructions

For this assignment, collect data exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, findr²(coefficient of determination) andr(correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below.

ALinear Model ExampleandTechnology Tips are provided in separate documents.

Tasks for Linear Regression Model (LR)

(LR-1)Describe yourtopic, provide yourdata, and cite yoursource.Collect at least 8 data points.Label appropriately.(Highly recommended: Post this information in the Linear Model Project discussion as well as in your completed project.Include a brief informative description in the title of your posting.Each student must use different data.) The idea with the discussion posting is two-fold: (1) To share your interesting project idea with your classmates, and (2) To give me a chance to give you a brief thumbs-up or thumbs-down about your proposed topic and data. Sometimes students get off on the wrong foot or misunderstand the intent of the project, and your posting provides an opportunity for some feedback. Remark:Students may choose similar topics, but must havedifferent data sets. For example, several students may be interested in a particular Olympic sport, and that is fine, but they must collect different data, perhaps from different events or different gender.

(LR-2)Plot the points (x,y) to obtain ascatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully.Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.)

(LR-3)Find theline of best fit(regression line) andgraphit on the scatterplot.State theequationof the line.

(LR-4)State theslopeof the line of best fit. Carefullyinterpretthe meaning of the slope in a sentence or two.

(LR-5)Find and state the value ofr², the coefficient of determination, andr, the correlation coefficient. Discuss your findings in a few sentences. Isrpositive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?

(LR-6)Choose a value of interest and use the line of best fit to make anestimate or prediction. Show calculation work.

(LR-7)Write a briefnarrativeof a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line,r, or estimate, etc.) that you found particularly important or interesting.

You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.